Rozzer has run inside: crime writer almost catching us in college (6,7)
I believe the answer is:
corpus christi
'us in college' is the definition.
'corpus christi' can be an answer for 'college' (name of colleges at Oxford and Cambridge). I am unsure of the 'us in' bit.
'rozzer has run inside crime writer almost' is the wordplay.
'rozzer has' becomes 'copus' (I am not sure about this - if you are sure you should believe this answer much more).
'run' becomes 'r' (cricket abbreviation).
'inside' indicates putting letters inside.
'crime writer' becomes 'Christie' (Agatha Christie).
'almost' means to remove the last letter (most of the word but not all of it).
'copus' placed around 'r' is 'corpus'.
'christie' with its final letter removed is 'christi'.
'corpus'+'christi'='CORPUS CHRISTI'
'catching' acts as a link.
(Other definitions for corpus christi that I've seen before include "Church festival; Oxford college" , "Texan city: name shared by colleges at Oxford and Cambridge" , "Oxbridge college" , "Oxford or Cambridge college" .)